#179

Dear Jakub Wieckowski,Paweł Białn,Wojciech Sałabun

I read your paper:

Comparative sensitivity analysis of single and multiple modifications in multi-criteria decision analysis

My comments

1- In the abstract you say “Recognizing the unexplored potential in sensitivity analysis, the study proposed a novel approach of simultaneous modification of multiple values in decision matrix, offering an extension CRIW) method for weighting criteria in the decision problem and applied it to support customers in ranking products (Dahooie et al. 2021)¨

1.1 Pls consider that there are MCDM methods like SIMUS, that was published in a book in 2019, addressing that issue of simultaneous modifications, and therefore, your paper appears not to be a novel approach.

1.2 I am happy that finality SOMEBODY addressed the issue of simultaneous variation of several criteria in sensitivity analysis (SA), since it is common practice the procedure of varying one-at-a-time, which is utterly erroneous.

However, in my opinion, the paper which is indeed a great contribution, is missing two important concepts:

If it is true that all alternatives are subject to a set of criteria when a solution is reached, please consider that:

1- Only some of the criteria are relevant for a certain solution, and this relevance is particular of each solution, thus, it is not equal for all alternatives, whatever their position in the ranking. In all cases these relevant criteria are called ‘basic criteria”, because a variation in any of them may affect the strength of the corresponding alternative. The other non-basic criteria are irrelevant, since whatever their variation it does not affect the alternatives. This can be easily proved in any computer using Excel.

Therefore, you need to identify which are those relevant criteria.

2- You are assigning arbitrary values in both, increasing and decreasing, assuming that you can select them between certain limits that you establish, which I consider incorrect. That is, each basic criterion normally has a pair of limiting values, low and high. If the DM surpasses them, that criterion ceases to be basic and then qualifies as irrelevant, and conversely and irrelevant criterion becomes basic.

Therefore, those limits are not determined subjectively, but following a mathematical procedure.

These facts may happen, say that we consider three basic criteria like C4, C7 and C10 out of a total of 15. Consider that:

- The three criteria posses a considerable gap between these limiting values. In this case we can safely say that the respective alternative is strong

- If say, C4 calls for maximization, we are interested in knowing which is the highest value, and if it is large, then, again thrse alternative is strong. The same concept applies to C7 and C10, irrelevant if they call for max or min. It can be for instance that C10 has no gap, i.e., zero. Then, the corresponding alternative is in a dangerous position, since the minimum variation may produce it losing its position, and the ranking. Same for C7

Therefore, for the alternative to be strong, these three criteria must have a reasonable gap. What is ‘reasonable’? Say for instance than C7 refers to international prices of a good; if statistics show that they have a very sharp variation in plus and minus in a period; the DM may decide that this involves high risk, or perhaps not. If he decides that it has a great risk most probably, he will recommend the stakeholders to select another less risky alternative. This is not subjective, for it is based on statistical trends, appreciation of the international situation, research, consultation, etc. i.e., it will be a decision taken considering and studying the performance of exogenous variables.

This is not a blackboard example; it is real, and present nowadays with a company exporting wheat, maize and soy for instance. The most profitable grain is soy, but at present its price is very low, and then, farmers prefer to export wheat and maize, which are less risky, and keep their soy in silos until the situation improves

I solved your exercise in Table 4 using SIMUS and without weights, and the result shows that the most important alternatives are both, A1 and A2, for they have the same scores, 0. 33 each.

This solution for both maximizing criteria, is very strong, since computation shows that in maximizing the DM can increase them is as much as he wants, and a lower limit of 0.56, and for A2 a lower limit of 0.50. Sometimes in both maximization or minimization, the corresponding criterion is blocked, in the sense that it does not have an allowable variation. All this information can be seen in SIMUS last screen. Alternatives A3 and A4, are no solutions, since they do not depend on any basic criteria

As a last point, SIMUS informs that criterion C1 (whatever it refers to), when increased in one unit, has a marginal value of 4.08 to improve utility Z3 (whatever it can be), and that criterion C3 (whatever it refers to), when increased in one unit, has a marginal valuer of 2.45 to improve utility of objective Z1(whatever it can be).

Consequently, progressively varying both criteria, always within their limits, allows to have the total utility of the project. This information is automatically produced by IOSA (Input-Output Sensitive Analysis), a SIMUS add-in, drawing the total utility curve, using scientific data. In turn, comparing these curves and statistical and analysis it is possible to compute the risk due to exogenous variables.

There is no value for C2, and for C3 a marginal value of 2.45. These marginal values are not weights but indicate the importance of each criterion relative to the utility of the objective represented by objective C1

Of course, the authors will realize that these marginals values are the ‘shadow prices”, of Linear Programming, that also allow to compute the value of intangibles or externalities that do not have a market value. For insgtancein co mputing throe GDPno country considers the costs of mines depletion in the extraction unit, the noise in highways or the wrong use of aquifers. Please note that this is 100% mathematics, since no value from the DM has been inputted,

However, it allows the DM to apply his experience and knowledge based on external factors, and modify the result, something that the software cannot do.

Naturally, as you say, the basic criteria must be applied simultaneously whatever their call and mixing between max and min.

Dear authors, please consider that it is far from my mind and purpose, to lecture anybody, let alone learned colleagues. The only reason by which I expand my comments is that I want to justify what I say or wright. If I am mistaken, I will welcome criticism or discussion either in public by RG or private by e mail

Nolberto Munier